For a general quiver with potential \((Q,W)\) , the determination of the initial rays is a difficult problem.
For an acyclic quiver however, it is easy to prove that the only initial rays are those associated to the
simple representations at each node [1]}, with
\(\Omega _\star (\gamma _i)=1, \quad \Omega _\star (k\gamma _i)=0 \ \mbox{for}\ k>1\) 
